Typical Eddy Research Articles

Observation of Statistical Characteristics and Vertical Structures of Surface Warm Cyclonic Eddies and Cold Anticyclonic Eddies in the North Pacific Subtropical Countercurrent Region

Conventional wisdom about mesoscale eddies is that cyclonic (anticyclonic) eddies are commonly associated with cold(warm) surface cores. Nevertheless, plenties of surface warm cyclonic eddies (WCEs) and cold anticyclonic eddies (CAEs) in the North Pacific Subtropical Countercurrent (STCC) region are observed by a synergistic investigation based on data from satellite altimetry, microwave radiometer, and Argo float profiles in this study. The results indicate that these two types of abnormal eddies (WCEs and CAEs) are prevalent in the STCC region, comprising approximately 30% of all eddies detected via satellite observations. We then analyze their spatial-temporal distribution characteristics and composite vertical structures. A statistical comparison with surface cold cyclonic eddies (CCEs) and warm anticyclonic eddies (WAEs) reveals notable differences between the anomalous and typical eddies. Additionally, we present the composite vertical structures of temperature and salinity anomalies for the anomalous eddies across five delineated subregions within an eddy-coordinate system. Furthermore, the close relationship between these abnormal eddies and subsurface-intensified mesoscale eddies are discussed.

Three-dimensional temperature field inversion in the northern South China Sea

A Swin Transformer oceanic three-dimensional temperature field inversion model is established for the northern South China Sea and its surrounding waters based on satellite observation data and ocean reanalysis data from 1993 to 2018. The inversion results are tested using Argo observation data. The root-mean-square errors of the monthly average temperature fields for 2017 and 2018 are 0.10 to 1.98°C and 0.11 to 1.92°C, respectively, with the maximum values mainly located near the mixing layer. The temperature inversion root-mean-square errors are generally less than 1 °C. Additionally, this article analyzes the three-dimensional structural characteristics and evolution process of a typical anticyclone eddy in the study area. The results show that the inversion results can clearly demonstrate the three-dimensional structure of the eddy and continuously and completely reproduce the process of eddy persistence and movement.

Effect of a cyclonic eddy on phytoplankton: A bioassay experiment

AbstractCyclonic eddies often increase the primary productivity of marine ecosystems. However, the study of their influence on the taxonomic structure and productivity of plankton is complex due to the short‐term and mesoscale nature of the action of eddies. In a laboratory bioassay experiment, we simulated two mechanisms of eddy's effect on the deep phytoplankton maximum: an increase in the upward flow of deep nutrients and illumination. Doubling of nutrient additions compared to control increased chlorophyll's specific growth rate (SGR) 1.7‐fold over 12 days while doubling the light intensity increased SGR by 3.5 times. During the first 4 days of the experiment, at the exponential growth stage, SGR of carbon biomass was maximum with the simultaneous doubling of nutrients and light (0.44 day−1). It was statistically significantly higher than at increased nutrients but not light. These results suggest that nutrient deficiencies were less crucial for phytoplankton growth than light. The increase in the phytoplankton biomass was mainly due to the growth of a large‐celled diatom Pseudosolenia calcar‐avis. It showed the highest SGR (1.15–1.28 day−1) at increased nutrients and/or light, resulting in high wet biomass of 2–3 g m−3 over 4 days. The ecological meaning of the obtained results is as follows. First, in the eddy, where the deep phytoplankton maximum is located close to the nutricline, its rise to more illuminated layers results in higher phytoplankton growth than the shortening distance to the nutricline. Second, increases in the upward flow of nutrients and light intensity, separate or simultaneous, stimulate the rapid reproduction of large‐celled diatoms that increase the carbon‐to‐chlorophyll ratio by 2–4 times. Third, exposure to a typical Black Sea mesoscale cyclonic eddy can lead to phytoplankton blooms in the thermocline within a few days.

Eddy Acceleration and Decay Driven by Internal Tides

Abstract Recent observations and numerical simulations have demonstrated the potential for significant interactions between mesoscale eddies and smaller-scale tidally generated internal waves—also known as internal tides. Here, we develop a simple theoretical model that predicts the one-way upscale transfer of energy from internal tides to mesoscale eddies through a critical level mechanism. We find that—in the presence of a critical level—the internal tide energy flux into an eddy is partitioned according to the wave frequency Ω and local inertial frequency f: a fraction of 1 − f/Ω is transferred to the eddy kinetic energy, while the remainder is viscously dissipated or supports mixing. These predictions are validated by comparison with a suite of numerical simulations. The simulations further show that the wave-driven energization of the eddies also accelerates the onset of hydrodynamical instabilities and the breakdown of the eddies, thereby increasing eddy kinetic energy, but reducing eddy lifetimes. Our estimates suggest that in regions of the ocean with both significant eddy fields and internal tides—such as parts of the Gulf Stream and Antarctic Circumpolar Current—the critical level effect could drive a ∼10% month−1 increase in the kinetic energy of a typical eddy. Our results provide a basis for parameterizing internal tide–eddy interactions in global ocean models where they are currently unrepresented.

On wall pressure fluctuations in conical shock wave/turbulent boundary layer interaction

The structure and the frequency spectra of wall pressure fluctuations beneath a planar turbulent boundary layer interacting with a conical shock wave at Mach number $M_\infty =2.05$ and Reynolds number $\textit {Re}_\theta \approx 630$ (based on the upstream boundary layer momentum thickness) are examined to elucidate the effects of pressure gradient and flow separation on the characteristics of the wall pressure fluctuations, by exploiting a direct numerical simulation database. Upstream of the interaction, in the zero pressure gradient region, wall pressure statistics compare well with canonical compressible boundary layers in terms of fluctuation intensities and frequency spectra. Across the main interaction zone (APG1), the root-mean-square of wall pressure fluctuations becomes very large (corresponding to approximately 173.3 dB), with maximum increase approximately 12.7 dB from the incoming level. In the second adverse pressure gradient zone (APG2), the root-mean-square of wall pressure fluctuations attains a second peak (corresponding to $164.7$ dB), with an increase of 8.4 dB from the upstream level. Both the APG1 and APG2 regions feature a substantial fraction of flow reversal events, which are, however, scattered and interspersed with regions of attached flow. The wall pressure power spectral density exhibits a broadband and energetic low-frequency component associated with the global unsteadiness of the separation bubble/conical shock system. Analysis of the two-point correlations and wavenumber/frequency spectra of wall pressure fluctuations further suggests that the typical eddies become more elongated along the spanwise direction, as the flow in the separated region tends to escape the centreline, and the convection velocity is significantly reduced.

Relationship between global ocean mixing and coherent mesoscale eddies

Numerous studies have indicated that mesoscale eddies play an important role in diapycnal mixing and drive global water circulation. Although the relationships between eddy surface features and turbulent mixing have been discussed for individual cases of typical eddies, global studies cannot rely on ship-based microstructural measurements. Fine-scale methods have been developed, wherein either the vertical shear of velocity or density strain is used to estimate turbulent mixing. In this study, the turbulent dissipation rate was estimated using strain information from Argo floats trapped in eddies. Spatially averaged estimates revealed the global distribution patterns of the dissipation rates inside the eddies. In addition, the relationships between eddy features (polarity, radius, vertical extent, and aspect ratio) and turbulent dissipation rates were analyzed. Three main conclusions were made from this study. First, turbulent dissipation rates inside anticyclones were generally larger than those inside cyclones. Second, turbulent dissipation rates inside eddies are related to their vertical extent but not to their horizontal scale. For shallow eddies (with a vertical extent less than 250 m for cyclones and 1000 m for anticyclones), the deeper the vertical extent, the larger the turbulent dissipation rate. Finally, the relationship between the eddy aspect ratio and turbulent dissipation rate was characterized by skewness. The average turbulent dissipation rate reached a maximum value when the cyclone aspect ratio was approximately 0.007; conversely, no maximum value was reached for anticyclones. This work establishes a correlation between eddy features and turbulent dissipation rates, which will help guide numerical simulations of mesoscale eddies.

Eddy Deformation and Kinetic Energy Conversion During the Eddy‐Kuroshio Interaction East of Taiwan

AbstractEddy‐mean flow interactions have always been of interest to researchers because they are among the causes of energy cascades. Different from most previous studies, this research concentrates on the Kuroshio Current's effect on an eddy during multiple independent elliptical eddy‐Kuroshio interactions. Eddy deformation during the eddy‐Kuroshio interaction is applied as the statistical criterion to select the typical eddies that interact with the Kuroshio east of Taiwan. There are 9 anticyclonic eddies (AEs) and 15 cyclonic eddies (CEs) that satisfy the criteria from the 1993 to 2018 satellite altimeter data. The blocking effect caused by the anti‐phase velocity at the contact interface of the CE and Kuroshio results in the eddy kinetic energy (EKE) at the CE edge being obviously inhomogeneous, while the AE does not result in the same effect. Moreover, the temporal variation in EKE during the eddy‐Kuroshio interaction precedes the AE/CE deformation by approximately 0.55/0.27 interaction cycles. The Kuroshio has different modulation mechanisms for different eddy polarities. Barotropic and baroclinic instabilities contribute to the generation of EKE, with barotropic instabilities providing more than 10 times as much as baroclinic instabilities for the AE and 4 times as much for the CE. The advection effect of the AE on the Kuroshio is in anti‐phase with the effect of the Kuroshio on the AE, which eventually makes the AE shrink. They are in phase for the CE and lead the CE to eventually become meandering.

COVID-19 pandemic underscores role of green space in urban carbon dynamics

For Detroit Michigan the arrival of COVID-19 led to intensive measures to prevent further spread of the virus resulting in consequent changes in traffic and energy use. We take advantage of these different emission scenarios to explore CO2 dynamics in a postindustrial city with a declining population and increasing green space. We present atmospheric CO2 concentration and net urban ecosystem exchange of CO2 (NUE) from a typical eddy covariance system and canopy greenness from a field camera on the Wayne State University campus in midtown Detroit. We categorized our study period (January 18, 2020–July 31, 2020) into three subperiods associated with the state-wide shelter-in-place order. Our results support that the city was a net carbon source throughout the period, particularly during the shelter-in-place period, although reduced traffic lowered CO2 concentrations and NUE. However, during the post-order period when traffic was highest, atmospheric CO2 concentrations and NUE were lowest, suggesting that the greening of urban vegetation may have greater carbon mitigation potential than lowering anthropogenic carbon emissions through traffic reductions.

Prediction of Changeable Eddy Structures around Luzon Strait Using an Artificial Neural Network Model

Mesoscale eddies occur frequently in the Luzon Strait and its adjacent area, and accurate prediction of eddy structure changes is of great significance. In recent years, artificial neural network (ANN) has been widely applied in the study of physical oceanography with the continuous accumulation of satellite remote sensing data. This study adopted an ANN approach to predict the evolution of eddies around the Luzon Strait, based on 25 years of sea level anomaly (SLA) data, 85% of which are used for training and the remaining 15% are reserved for testing. The original SLA data were firstly decomposed into spatial modes (EOFs) and time-dependent principal components (PCs) by the empirical orthogonal function (EOF) analysis. In order to calculate faster and save costs, only the first 35 PCs were selected as predictors, whereas their variance contribution rate reached 96%. The results of predicted reconstruction indicated that the neural network-based model can reliably predict eddy structure evaluations for about 15 days. Importantly, the position and variation of four typical eddy events were reconstructed, and included a cyclone eddy event, an eddy shedding event, an anticyclone eddy event, and an abnormal anticyclone eddy event.

The Analytical Comparative Analysis of Electromagnetic Characteristics of Four Typical Radial Flux Permanent Magnet Eddy Current Couplers

The analytical model of a permanent magnet eddy current coupler (PMECC) is mainly used for evaluation of its characteristics and the initial optimization of design. Based on the equivalent magnetic circuit method, this paper carries out analytical modeling for four typical PMECCs composed of surface-mounted and interior permanent magnet, slotted and non-slotted conductor rotors, which provides a theoretical basis for the subsequent research in this paper. The basic electromagnetic characteristics of the PMECCs are investigated by the established analytical model. Simultaneously, the analytical results about permeance, flux density, torque and power are verified by FEA simulation. The analysis results show that the slotted CR will obtain a much higher power density, and the iron loss mainly exists in the CRs. In addition, the analytical and FEA results agree well, which proves the reliability of the proposed, nearly unified analytical model.

A Thermal Drift Compensation Method for Precision Sensors Considering Historical Temperature State

This article proposes a compensation method for precision sensors considering historical temperature states, which can significantly reduce the thermal drift of the sensors during rapid temperature change process. A typical differential eddy current sensor (ECS) measuring displacement is used as an example to explain the principle. By analyzing the source of thermal drift of the ECS, it is proved that time history of temperature change will also affect the output of the ECS. In this article, the temperature response characteristics of the sensing head of the ECS are obtained by the lumped capacitance method, and the output of the ECS is compensated by convolution operation. Experimental results show that the temperature coefficient of the ECS during a temperature change process is depressed from 34.62 to 1.64 nm/°C with this method, and it is also less than 1/4 of 7.70 nm/°C which is obtained with direct compensation using current temperature value. Furthermore, this method is expected to function efficiently for any precision sensor in complex and harsh temperature environments.

Submesoscale Fronts and Their Dynamical Processes Associated with Symmetric Instability in the Northwest Pacific Subtropical Ocean

AbstractSubmesoscale density fronts and the associated processes of frontogenesis and symmetric instability (SI) are investigated in the northwest Pacific subtropical countercurrent (STCC) system by a high-resolution simulation and diagnostic analysis. Both satellite observations and realistic simulation show active surface fronts with a horizontal scale of ~20 km in the STCC upper ocean. Frontogenesis-induced buoyancy advection is detected to rapidly sharpen these density fronts. The direct straining effect of larger-scale geostrophic flows is a primary influence on the buoyancy-gradient frontogenetic tendency and frontal baroclinic potential vorticity (PV) enhancement. The enhanced lateral buoyancy gradients in conjunction with atmospheric forced surface buoyancy loss can produce a negative Ertel PV and trigger frontal SI in the STCC region. Up to 30% of the mixed layer (ML) inside a typical eddy has negative PV in the high-resolution simulation. As a result, the cross-front ageostrophic secondary circulations tend to restratify the surface boundary layer and induce a large vertical velocity reaching ~100 m day−1, substantially facilitating the vertical communication of the STCC system. At the same time, the SI is identified to be responsible for a forward cascade of geostrophic kinetic energy in the STCC region, despite the coexistence of ML eddies and SI in the deep winter ML. Therefore, these active density fronts and their SI-associated submesoscale processes play important roles in the enhanced vertical exchanges (e.g., heat, nutrients, and carbon) and energy transfer to smaller scales in the eddy-active STCC upper ocean, as well as triggering phytoplankton blooms at the periphery of eddies.

Surface water exchanges in the Luzon Strait as inferred from Lagrangian coherent structures

This study presents a Lagrangian view of upper water exchanges across the Luzon Strait based on the finite-time Lyapunov exponents (FTLE) fields computed from the surface geostrophic current. The Lagrangian coherent structures (LCSs) extracted from the FTLE fields well identify the typical flow patterns and eddy activities around the Luzon Strait. In addition, they reveal the intricate transport paths and fluid domains, which are validated by the tracks of satellite-tracked surface drifters and cannot be visually recognized in the velocity maps. The FTLE fields indicate that there are mainly four types of transport patterns near the Luzon Strait; among them, the Kuroshio northward-flowing “leaping” pattern and the clockwise rotating “looping” pattern occur more frequently than the “leaking” pattern of the direct Kuroshio branch into the SCS and the “outflowing” pattern from the SCS to the Pacific. The eddy shedding events of the Kuroshio at the Luzon Strait are further analyzed, and the importance of considering LCSs in estimating transport by eddies is highlighted. The anticyclonic eddy (ACE) shedding cases reveal that ACEs mainly originate from the looping paths of Kuroshio and thus could effectively trap the Kuroshio water before eddy detachments. LCSs provide useful information to predict the positions of the upstream waters that finally enter the ACEs. In contrast, LCS snapshots indicate that during the formation of cyclonic eddies (CEs), most CEs are not connected with the pathways of Kuroshio water. Hence, the contribution of CEs to the surface water exchanges from the Pacific into the SCS is tiny.

Influence of mesoscale eddies on cross-shelf exchange in the western Gulf of Mexico

This study uses ROMS (Regional Ocean Modeling System) with realistic forcing to analyse cross-shelf transport associated with the presence of mesoscale anticyclones as they interact with the western shelf of the Gulf of Mexico. Daily outputs from this validated 15-year numerical simulation were used to calculate the depth and time averaged cross-shelf volume transport through the 200 m isobath, used as a proxy for the shelf break. Composites for cases in which mesoscale anticyclones (MAs) are close or far away from the shelf break were performed to show that cross-shelf exchange has remarkable differences when they interact with the shelf. These differences consist of: a) enhanced off-shelf transport on its northern rim (at ~ 25.5oN), b) a flow with multiple inversions associated with the main body of the MA where both on and off-shelf transports are considerably increased, and c) enhanced on-shelf transport at its southern edge, linked to the interaction of the MA with the persistent mesoscale cyclonic circulation in the Bay of Campeche. The multiple transport inversions associated with the main body of the MA is clearly linked with spatial patterns of baroclinic and barotropic instabilities that develop at the rings edge. The time-evolution of a representative event in which an MA interacts with the shelf is analysed to verify the influence on cross-shelf transport observed in the composites. Results show that enhanced cross-shelf transport is driven by the proximity, shape, and angle of orientation of the anticyclone with respect to the shelf. The Eulerian analysis of the event coincides with the composite results described above with enhanced cross-shelf exchange when the MA is rounder and closer to the shelf. A Lagrangian experiment is carried out to quantify the exchange and fate of particles during this “typical eddy event”, seeding drifters within the shelf, inside the MA and in the open waters outside the eddy. Results show a substantial increase in exchange rate and distance traveled by particles (they travel 200 km farther) when the MA is closer to the shelf.

Observation and Lagrangian Analysis of Quasi‐Stationary Kamchatka Trench Eddies

AbstractBased on satellite altimeter data for the last 25 years, an area over the Kuril‐Kamchatka Trench (KKT) was found near the southern tip of Kamchatka Peninsula where mesoscale anticyclonic eddies have stalled for a long period of time. Using altimetry‐based Lagrangian maps, we detected 24 quasi‐stationary Kamchatka trench eddies (KTEs). Their genesis is related to anticyclonic eddies generated in the Kamchatka bays. After reaching the western slope of the KKT, those eddies slowdown and stagnate there. During the stagnation phase, all the KTEs were found to merger with anticyclonic eddies advected from the north. This feed up was accompanied by a significant increase of the KTEs in size and eventually by their destabilization. By arranging the data in Hovmöller diagrams, we got spatial patterns of the variability in the eddy kinetic energy and vorticity in the altimetry era. The typical eddy in this family KTE2017 has stagnated in the catching area during 8 months and was sampled in September 2017 in a cruise. The conductivity, temperature, pressure (CTD) measurements and Argo T/S vertical profiles demonstrated a typical subarctic vertical structure of water masses in summer. Different kinds of Lagrangian indicators were computed to study the life cycle of KTE2017. The KTE2017 during the stagnation phase of its life was found to be a shielded anticyclonic vortex surrounded by smaller‐scale cyclones. This configuration maintained its stability and stagnation over the KKT. We discuss different reasons by which KTE2017 and other KTEs have stagnated in the catching area.

Comparison of Remotely Sensed Evapotranspiration Models Over Two Typical Sites in an Arid Riparian Ecosystem of Northwestern China

Accurate estimates of evapotranspiration (ET) are essential for the conservation of ecosystems and sustainable management of water resources in arid and semiarid regions. Over the last two decades, several empirical remotely sensed ET models (ERSETMs) had been developed and extensively used for regional-scale ET estimation in arid and semiarid ecosystems. These ERSETMs were constructed by combining datasets from different sites and relating measured daily ET to corresponding meteorological data and vegetation indices at the site scale. Then, regional-scale ET on a pixel basis can be estimated, using the established ERSETMs. The estimation accuracy of these ERSETMs at the site scale plays a fundamental and crucial role in regional-scale ET estimation. Recent studies have revealed that ET estimates from some of these models have significant uncertainties at different spatiotemporal scales. However, little information is available on the performance of these ERSETMs at the site scale. In this study, we compared eight ERSETMs, using ET measurements from 2013 to 2018 for two typical eddy covariance sites (Tamarix site and Populus site) in an arid riparian ecosystem of Northwestern China, intending to provide a guide for the selection of these models. Results showed that the Nagler-2013 model and the Yuan-2016 model outperformed the other models. There were substantial differences in the ET estimation of the eight ERSETMs at daily, monthly, and seasonal scales. The mean ET of the growing season from 2013 to 2018 ranged from 465.93 to 519.65 mm for the Tamarix site and from 386.22 to 437.05 mm for the Populus site, respectively. The differences in model structures and characterization of both meteorological conditions and vegetation factors were the primary sources of different model performance. Our findings provide useful information for choosing models and obtaining accurate ET estimation in arid regions.

Eddy‐Driven Cross‐Shelf Transport in the East Australian Current Separation Zone

AbstractIn western boundary current systems, sharp velocity gradients between the poleward flowing jet and coastal waters generally act to inhibit cross‐shelf exchange. Downstream of jet separation, dynamic mesoscale eddies dominate the flow. In the East Australian Current System, counter‐rotating eddy dipoles are often present which, in the appropriate configuration, have potential to drive cross‐shelf transport. However, this eddy dipole mode is poorly understood in the framework of cross‐shelf exchange and the effect of these structures on shelf waters is uncertain. Using 25 years of satellite altimetry, as well as in situ sampling of a typical dipole event, we investigate the characteristics of eddy‐driven cross‐shelf exchange. We show that the maximum onshore velocity is driven by an eddy dipole structure and occurs in a defined latitudinal band between 33°S and 34°S more than 50% of the time. We sample a typical eddy dipole and find a strong onshore jet, 37 km wide, with velocities up to 1.78 m s and a transport of at least 16 Sv. Hydrographic data from an autonomous underwater glider show that this jet manifests on the shelf as a subsurface intrusion of warm salty water extending from offshore up onto the midshelf. In the light of climatic changes in western boundary current transport and the increase in their eddy kinetic energy, understanding eddy‐driven cross‐shelf exchange is important to predict future changes to the shelf water mass.

The Difference of Sea Level Variability by Steric Height and Altimetry in the North Pacific

Sea level variability, which is less than ~100 km in scale, is important in upper-ocean circulation dynamics and is difficult to observe by existing altimetry observations; thus, interferometric altimetry, which effectively provides high-resolution observations over two swaths, was developed. However, validating the sea level variability in two dimensions is a difficult task. In theory, using the steric method to validate height variability in different pixels is feasible and has already been proven by modelled and altimetry gridded data. In this paper, we use Argo data around a typical mesoscale eddy and altimetry along-track data in the North Pacific to analyze the relationship between steric data and along-track data (SD-AD) at two points, which indicates the feasibility of the steric method. We also analyzed the result of SD-AD by the relationship of the distance of the Argo and the satellite in Point 1 (P1) and Point 2 (P2), the relationship of two Argo positions, the relationship of the distance between Argo positions and the eddy center and the relationship of the wind. The results showed that the relationship of the SD-AD can reach a correlation coefficient of ~0.98, the root mean square deviation (RMSD) was ~1.8 cm, the bias was ~0.6 cm. This proved that it is feasible to validate interferometric altimetry data using the steric method under these conditions.

Submesoscale Features and Turbulent Mixing of an Oblique Anticyclonic Eddy in the Gulf of Alaska Investigated by Marine Seismic Survey Data

AbstractMesoscale eddies are ubiquitous in the global ocean and can be captured by marine multichannel seismic surveys. In this study, a short‐lived anticyclonic eddy is characterized along the seismic line STEEP11 acquired on 30 September 2008 in northern Gulf of Alaska. Fine‐scale eddy stratification with alternative strong striae and weak layers is regarded as a typical eddy structure of the study region. The eddy center dips along a NW tilted axis of 1.9 ± 0.2° from the horizontal. Submesoscale structures including fronts and filaments coexist around the eddy periphery and dominate ~70% of the eddy volume. The estimated geostrophic current is asymmetric and ageostrophic components must play a significant role in balancing the eddy system. Nonlinearity of the eddy is strong as its rotation speed is much higher than its translation speed. We suggest that Ekman transport is probably responsible for the skewed shape with regards to the asymmetric geostrophic current and asymmetric submesoscale processes. Detailed turbulent diffusivities in and around the eddy are quantified, with an average level of 6.5 × 10−5 m2 s−1. The diapycnal diffusivities show an increasing pattern from the eddy center to the surrounding water. With the pervasive submesoscale processes as the transitional dynamics, a forward cascade of energy could be expected from the mesoscale eddy to the fine‐scale wave‐breaking and turbulence. The irregular vortex structure may reduce the structural stability, facilitate the energy conversion, and accelerate the eddy dissipation.

Rossby-number effects on columnar eddy formation and the energy dissipation law in homogeneous rotating turbulence

Two aspects of homogeneous rotating turbulence are quantified through forced direct numerical simulations in an elongated domain, which, in the direction of rotation, is approximately 340 times larger than the typical initial eddy size. First, by following the time evolution of the integral length scale along the axis of rotation , the growth rate of the columnar eddies and its dependence on the Rossby number is determined as for , where is the non-dimensional growth rate. Second, a scaling law for the energy dissipation rate is sought. Comparison with current available scaling laws shows that the relation proposed by Baqui & Davidson (Phys. Fluids, vol. 27(2), 2015, 025107), i.e. , where is the root-mean-square velocity, approximates well part of our data, more specifically the range . However, relations proposed in the literature fail to model the data for the second and most interesting range, i.e. , which is marked by the formation of columnar eddies. To find a similarity relation for the latter, we exploit the concept of a spectral transfer time introduced by Kraichnan (Phys. Fluids, vol. 8(7), 1965, p. 1385). Within this framework, the energy dissipation rate is considered to depend on both the nonlinear time scale and the relaxation time scale. Thus, by analysing our data, expressions for these different time scales are obtained that result in , where is the integral length scale in the direction normal to the axis of rotation and is the nonlinear time scale of the initial homogeneous isotropic field.